Related papers: Contact surgery numbers
A knot in the 3-sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, i.e. a rational homology 3-sphere with the smallest possible Heegaard Floer homology. Given a knot K, take an unknotted circle c…
We show that a contact $(+1)$-surgery along a Legendrian sphere in a flexibly fillable contact manifold ($c_1=0$ if not subcritical) yields a contact manifold that is algebraically overtwisted if the Legendrian's homology class is not…
The cosmetic surgery conjecture is a longstanding conjecture in 3-manifold theory. We present a theorem about exceptional cosmetic surgery for homology spheres. Along the way we prove that if the surgery is not a small seifert…
In this article, we find the complete list of all contact structures (up to isotopy) on closed three-manifolds which are supported by an open book decomposition having planar pages with three (but not less) boundary components. We…
Given an $n$-component link $L$ in any 3-manifold $M$, the space $\mathcal{L} \subset (\mathbb{Q}\cup \mkern-1.5mu\{\infty\})^n$ of rational surgery slopes yielding L-spaces is already fully characterized (in joint work by the author) when…
We describe Legendrian surgery diagrams for some horizontal contact structures on non-positive plumbing trees of oriented circle bundles over spheres with negative Euler numbers. As an application we determine Milnor fillable contact…
We define a general procedure extending surgery to manifolds with foliation or Haefliger structure. We find a single obstruction to foliation surgery along an attaching sphere. When unobstructed, the surgery can be chosen to preserve…
A regular fiber of the Seifert fibering of the Poincar\'e homology sphere admits a Dehn surgery to $L(2,1)\#L(3,2)\#L(5,4)$. We prove that this is the only knot in the Poincar\'e homology sphere with a surgery to a connected sum of more…
We compute the Ozsv\'ath--Szab\'o contact invariants for all tight contact structures on the manifolds -\Sigma(2,3,6n-1).
Boyer, Gordon, and Watson have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since Dehn surgeries on knots in $S^3$ can produce large families of…
We investigate the line between tight and overtwisted for surgeries on fibred transverse knots in contact 3-manifolds. When the contact structure $\xi_K$ is supported by the fibred knot $K \subset M$, we obtain a characterisation of when…
In this paper, we study contact structures on any open 3-manifold V which is the interior of a compact 3-manifold. To do this, we introduce proper contact isotopy invariants called the slope at infinity and the division number at infinity.…
We construct an open book decomposition compatible with a contact structure given by a rational contact surgery on a Legendrian link in the standard contact $S^3$. As an application we show that some rational contact surgeries on certain…
We produce a rational homology 3-sphere that does not smoothly bound either a positive or negative definite 4-manifold. Such a 3-manifold necessarily cannot be rational homology cobordant to a Seifert fibered space or any 3-manifold…
Let S^3_r(K) be the oriented 3--manifold obtained by rational r-surgery on a knot K in S^3. Using the contact Ozsvath-Szabo invariants we prove, for a class of knots K containing all the algebraic knots, that S^3_r(K) carries positive,…
Suppose that the 3-manifold M is given by integral surgery along a link L in S^3. In the following we construct a stable map from M to the plane, whose singular set is canonically oriented. We obtain upper bounds for the minimal numbers of…
We show that all positive contact surgeries on every Legendrian figure-eight knot in $(S^3, \xi_{\rm{std}})$ result in an overtwisted contact structure. The proof uses convex surface theory and invariants from Heegaard Floer homology.
Contact homology for Legendrian submanifolds in standard contact $(2n+1)$-space is rigorously defined using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex $n$-space. It provides new invariants of…
These are notes of a talk given at the Mathematische Arbeitstagung 2005 in Bonn. Following ideas of Ozbagci-Stipsicz, a proof based on contact Dehn surgery is given of Eliashberg's concave filling theorem for contact 3-manifolds. The role…
We use the combinatorial techniques of graphs of intersection to study reducible Dehn surgeries on knots in the three-sphere. In particular, in the event that a reducible surgery on a knot K in the three-sphere of slope r produces a…